Question

Ten members of Ms. Ramos' history class are seated together at the front of the atrium,as they are presenters at the Black History Month presentation in the atrium. Determine theprobability that two of the students, Sofia and Victoria, will not be seated together.

Answer 1

Given

Total members = 10

Find

probability that two of the students, Sofia and Victoria, will not be seated together.

Step-by-step explanation

total arrangement of 10 members =

`10!`

from the 10 members , taking the two students sofia ad victoria as one , so arrangement of 9 members is

`9!`

these two students can be permuted among themselves in 2 ways

so , total arrangement =

`2!\cdot9!`

therefore , the probability that two of the students, Sofia and Victoria, will be seated together. =

`(2\cdot9!)/(10!)=(2)/(10)=(1)/(5)`

so , required probability that two of the students, Sofia and Victoria, will not be seated together is 1 - 1/5 = 4/5

Final Answer

Therefore , the probability that two of the students, Sofia and Victoria, will not be seated together is 4/5